I am working on a project and would like to analyze strings of data to determine statistical differences in clusters of XY coordinate data. Specifically, I would like to be able to determine if string 1 is less dispersed than string 2.

I have made a mock dataset (attached) that illustrates the type of data I am looking to analyze. Additionally, I have attached a file that examples the methodology I would like to explore. Unfortunately, I'm still learning JMP Pro (I have JMP Pro 11.2) and haven't been able to figure out how to tackle this analysis.

I'm not exactly sure what you are interested in, but I will attach a JMP data table (BGC Mock Data 2.jmp) constructed from your mock data by stacking the X and Y columns. The table contains a few scripts. Here is what they do:

The Source script (select Edit) shows how the data table was constructed.

For the remaining scripts, select Run Script:

The Test of X, Y Dispersion for Each Bullet scripts tests to see if the X and Y deviations have equal variances for each bullet. None of these show a significant difference. The sample sizes are small, though, and the test is not very sensitive. To obtain the analysis, select Fit Y by X and enter Y = Data, X = Label, and Bullet in the By text box. Then select Unequal Variances from the red triangle menu.

The Test Across All Groups script combines the data and does a joint test for differences in variance across all groups, defined as a bullet/coordinate combination. Again, no significant difference, but the sample sizes are small. To obtain the analysis, select Fit Y by X and enter Y = Data, X = Group.

The Test of Common Standard Deviation script allows you to test for hypothesized value of the standard deviation. To do this from the Distribution menu, select Test Std Deviation and enter your own hypothesized value. This approach assumes a common value of the variance. The Hurley paper makes the very strong assumption of a circular normal distribution to describe the points, and this implies that the variances are equal. (This is a very strong assumption, so I hope it is substantiated. See below. The variances might also be equal without the strong assumption of a circular normal.)

Now, having done all of this, please look at the attached data table BGC Mock Data 1.jmp. Run the script. It shows a scatterplot of the X and Y coordinates where the points are colored. There is a density ellipse for each bullet. The ellipses would suggest that the points don't follow a circular normal distribution. To better see the points, select Rows > Color or Mark by Column, select Bullet, check the box next to Make Window with Legend, and click OK. A Legend window appears. Click on the Bullet numbers to see them highlighted in the plot.